Actually, both Dokert AND Modessitt were offering very good advice for those monitors. On your 4600, the horizontal width coil was beginning to crumble. Bob Roberts has reclaimed coils (with the attached cradle to mount them) for $10.
As far as the neck glow goes on the 4600, it may not necessarily have been the flyback. Other components further back in the heater circuit may have been faulted, preventing the voltage from getting to the flyback and then to the heater in the tube.
Even if it WAS the flyback, there were still options. It just didn't seem like you were willing to explore them.
Tubes are a dime a dozen these days, with so many 19" TV's being sold cheap or given away on Craigslist. It's the chassis that are getting more valuable. The original 4900's, G07's and the like just don't compare to the repro junk that's being made now. And they were EASY to work on, provided you were diligent enough to follow logical troubleshooting.
The reason those two guys (and others) jumped all over you to send the chassis' to them was because you were starting to convey a tone of giving up and moving on. Since these guys would rather see the parts from these chassis benefit others, or even get fixed, they were trying to prevent valuable circuitry from being destroyed.
I can understand that you were looking to move on and free up space. But there are others in this community who have the space and willingness to pay for your shipping (and probably a bit more for your time) the parts to them.
Don't just throw stuff out. See if anyone here wants it first.